Sure it's observable. Record it and play back the film. They don't let you do that in a casino, so it's "random enough" for their purposes, but you can't turn a truly random process into a predictable one by observing it on a finer timescale.
You seem to be under the impression that observability creates non-randomness. It doesn't. It only creates non-randomness *if* observations done *before* the randomizing process can predict the results.
Suppose I had a device which used radioactive decay to produce perfect random whole numbers between 1 and any arbitrary number up to 52. I set an entire deck of cards in front of me, laid out side by side. I ask the device to pick a number from 1 to 52, take that card, and turn it over to one side. I then do the same again using a number between 1 and 51, placing the card face down on the first card. I continue, repeating until I have 52 perfectly chosen random cards stacked up next to me.
The deck is random, beyond any doubt, but anybody watching me knows exactly what order the deck was in. This ability to determine the final results by watching the randomizing process doesn't change the fact that it is a random result.
You can watch me shuffle from here to doomsday, but if your observations *before I begin* cannot tell you anything about the final result, this means nothing as to whether or not it is random. You have to predict the result, not observe it.
I'd disagree. It's a random system if knowing the state of the system at t0 doesn't allow you to predict the state of the system at t0+. The toss of a die might be "random in real time," because you can't predict it that way, but I'd dispute that it's random in the same way that, say, radioactive decay. Randomness is objective, not dependent on the observer, and there are theoretical observers who could predict the outcome of a die roll; there are no such observers for radioactive decay, or the emission of Hawking radiation, or of shot noise.
Nope. Not even a "perfect observer" could do what you describe, if the die roll is done correctly with sufficiently well-formed dice.
Quantum fluctuations influence the firing of my neurons in my brain and nerves, the twitching of my muscles, the elasticity of the dice impacts, and the movement of the molecules of the air. Further, a "perfect observer" who actually observed these quantum fluctuations would, according to quantum dynamics, inherently influence them, generating new randomness.
Further, the dice rolling is chaotic, with high sensitivity to initial conditions. Thus, even the tiniest random fluctuations in the base conditions produce completely different results. Since there is so much true unpredictability in the initial conditions, and so few possible results (only six per die), these tiny unpredictable factors translate to unpredictable macro effects.
In other words, even your "perfect observer" would still get a random result, if the die roll is rolled in such a way as to have both sufficient random fluctuations in the initial conditions and sufficient events that are sufficiently sensitive to initial conditions. However, it is theoretically possible for the perfect observer to spot when these factors do not apply, such as when a skilled dice thrower is throwing to minimize the randomizing effects.